Generalizations and Properties of the Multiscale Maxima and Zero-Crossings Representations

Simple item page
dc.contributor.advisorBaras, John S.en_US
dc.contributor.authorBerman, Zeeven_US
dc.contributor.departmentISRen_US
dc.date.accessioned2007-05-23T09:52:24Z
dc.date.available2007-05-23T09:52:24Z
dc.date.issued1992en_US
dc.description.abstractThe analysis of a discrete multiscale edge representation is considered. A general signal description, called an inherently bounded Adaptive Quasi Linear Representation (AQLR), motivated by two important examples, namely, the wavelet maxima representation, and the wavelet zero-crossings representation, is introduced. This thesis addresses the questions of uniqueness, stability, and reconstruction. It is shown, that the dyadic wavelet maxima (zero-crossings) representation is, in general, nonunique. Nevertheless, these representations are always stable. Using the idea of the inherently bounded AQLR, two stability results are proven. For a general perturbation, a global BIBO stability is shown. For a special case, where perturbations are limited to the continuous part of the representation, a Lipschitz condition is satisfied. Two reconstruction algorithms, based on the minimization of an appropriate cost function, are proposed. The first is based on the integration of the gradient of the cost function; the second is a standard steepest descent algorithm. Both algorithms are shown to converge. The last part of this dissertation describes possible modifications in the basic multiscale maxima representations. The main idea is to preserve the structure of the inherently bounded AQLR, while allowing a trade-off between reconstruction quality and amount of information required for representation. In particular, it is shown how quantization can be considered as an integral part of the representation.en_US
dc.format.extent8675577 bytes
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/1903/5317
dc.language.isoen_USen_US
dc.relation.ispartofseriesISR; PhD 1992-9en_US
dc.subjectsignal processingen_US
dc.subjectwavelet transformen_US
dc.subjectsignal representation en_US
dc.subjectreconstructionen_US
dc.subjectSystems Integrationen_US
dc.titleGeneralizations and Properties of the Multiscale Maxima and Zero-Crossings Representationsen_US
dc.typeDissertationen_US

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
PhD_92-9.pdf
Size:
8.27 MB
Format:
Adobe Portable Document Format
Download

Collections

Institute for Systems Research Technical Reports